CN118300546A - Broadband analog predistorter - Google Patents
Broadband analog predistorter Download PDFInfo
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- CN118300546A CN118300546A CN202410513817.2A CN202410513817A CN118300546A CN 118300546 A CN118300546 A CN 118300546A CN 202410513817 A CN202410513817 A CN 202410513817A CN 118300546 A CN118300546 A CN 118300546A
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Classifications
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03F—AMPLIFIERS
- H03F1/00—Details of amplifiers with only discharge tubes, only semiconductor devices or only unspecified devices as amplifying elements
- H03F1/32—Modifications of amplifiers to reduce non-linear distortion
- H03F1/3241—Modifications of amplifiers to reduce non-linear distortion using predistortion circuits
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03F—AMPLIFIERS
- H03F1/00—Details of amplifiers with only discharge tubes, only semiconductor devices or only unspecified devices as amplifying elements
- H03F1/42—Modifications of amplifiers to extend the bandwidth
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
- H03H7/00—Multiple-port networks comprising only passive electrical elements as network components
- H03H7/24—Frequency- independent attenuators
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
- H03H7/00—Multiple-port networks comprising only passive electrical elements as network components
- H03H7/42—Networks for transforming balanced signals into unbalanced signals and vice versa, e.g. baluns
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03F—AMPLIFIERS
- H03F2200/00—Indexing scheme relating to amplifiers
- H03F2200/36—Indexing scheme relating to amplifiers the amplifier comprising means for increasing the bandwidth
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Abstract
The invention discloses a broadband analog predistorter, which specifically comprises the following components: the broadband Marchand balun comprises a first three-coupling line broadband Marchand balun, a first tuning transmission line, an attenuator, a first phase shifter, a second tuning transmission line, a third tuning transmission line, a first blocking capacitor, a Schottky barrier diode, a second blocking capacitor, a second phase shifter, a fourth tuning transmission line, a second three-coupling line broadband Marchand balun, a direct current bias circuit and a second radio frequency choke inductance. The invention adopts a three-coupling line broadband Marchand balun, an actively biased Schottky barrier diode, an attenuator and a phase shifter to form a two-way structure, a signal is divided into two ways through the balun, one branch adopts the phase shifter and the attenuator as linear branches, the other branch adopts the Schottky barrier diode to generate nonlinear signals, the signals of the two branches are vector synthesized at the differential end of the balun, and the amplitude phase adjustment can be realized in a broadband by adjusting the bias voltage of the nonlinear branches, the attenuator of the linear branches and the phase shifter.
Description
Technical Field
The invention belongs to the technical field of microwave power amplifiers, and particularly relates to a broadband analog predistorter.
Background
With the development of modern wireless communication technology, in order to cope with the rapid increase in the number of user terminals and communication data traffic, complex digital modulation schemes like quadrature amplitude modulation (64-QAM) and multi-carrier transmission techniques like Orthogonal Frequency Division Multiplexing (OFDM) are widely used in modern wireless communication systems. The application of these techniques significantly improves spectral efficiency, but results in a higher peak-to-average power ratio (Peak to Average Power Ratio, PAPR) of the transmitted signal. The peak-to-average ratio signal is easier to make the power amplifier enter a saturated working area and generate nonlinear distortion, so that the power amplifier needs to have higher linearity. Currently, the main stream high power amplifier is of two types, namely a Solid State Power Amplifier (SSPA) and a traveling wave tube power amplifier (TWTA). The former is superior to the latter in terms of size, cost and efficiency, but linearity often cannot reach the level of SSPA, in cases where high power (> 100W) can be provided; in a low power region, the SSPA is superior to TWTA in all aspects, and the requirements of the millimeter wave wireless communication system on the two types of power amplification degrees are more and more severe. Linearization techniques have been developed to improve the linearity index of the amplifier. The most common linearization techniques at present include: feedforward techniques, negative feedback techniques, predistortion techniques, and the like. The analog predistortion technology circuit has the advantages of simple structure, low cost, high working frequency range and easy integration, and is widely applied to engineering practice.
The analog predistortion technique is a linearization technique that pre-compensates for the target power amplifier curve. The analog predistorter is divided into a series transmission type, a parallel transmission type, a bridge reflection type, a two-way type structure and the like according to different circuit structures, and a schottky barrier diode is mostly adopted as a nonlinear signal generating device to generate a curve with the characteristic opposite to that of a target power amplifier so as to realize linearization of the power amplifier.
At present, analog predistorters are mainly divided into four types: serial transmission, parallel transmission, bridge reflection and two-way structures. The transmission type analog predistorter has a simple structure, and mainly comprises a main transmission line and a power amplifier, wherein nonlinear devices are connected in series or in parallel to generate a predistortion curve complementary with nonlinear characteristics of the power amplifier; the bridge reflection type adopts a 3dB bridge structure, nonlinear devices are loaded on through and coupling ports of the bridge, and the combination of two paths of reflected signals is utilized to generate required transmission characteristics; the two-path analog predistorter is based on the theory of vector synthesis of two-path signals, a linear path is generally formed by a phase shifter and an attenuator, a nonlinear path is formed by a nonlinear device, and the required transmission characteristic is generated by vector synthesis of the two-path signals.
The two-way analog predistorter applied at present realizes better amplitude phase adjustment characteristic, but can only be realized in a narrower frequency band at present due to the bandwidth limitation of a bridge, is difficult to realize linearization requirement in the wider frequency band,
Disclosure of Invention
In order to solve the technical problems, the invention provides a broadband analog predistorter, which can compensate the distortion characteristics of SSPA by changing the circuit bias state, the phase shifter and the phase shift quantity, and adopts a two-way structure of a broadband balun, so that the frequency band of the analog predistorter is wider.
The invention adopts the technical scheme that: a broadband analog predistorter specifically comprises: the broadband Marchand balun comprises a first three-coupled line broadband Marchand balun 1, a first tuning transmission line 3, an attenuator 4, a first phase shifter 5, a second tuning transmission line 6, a third tuning transmission line 8, a first blocking capacitor 9, a Schottky barrier diode 10, a second blocking capacitor 11, a second phase shifter 12, a fourth tuning transmission line 13, a second three-coupled line broadband Marchand balun 14, a direct current bias circuit 15 and a second radio frequency choke inductance 19.
The radio frequency signal is input from a first three-coupling line broadband Marchand balun 1 single port and is marked as a radio frequency signal input port 2; one end of a differential end of the first three-coupling line broadband Marchand balun 1 is connected with one end of a first tuning transmission line 3; the other end of the first tuning transmission line 3 is connected with one end of the attenuator 4; the other end of the attenuator 4 is connected with one end of the first phase shifter 5; the other end of the first phase shifter 5 is connected with one end of a second tuning transmission line 6; the other end of the second tuning transmission line 6 is connected with one end of a differential end of a second coupling line broadband Marchand balun 14; the single port of the second three-coupling line broadband Marchand balun 14 is used as a radio frequency signal output end and is marked as a radio frequency signal output port 7; one end of the third tuning transmission line 8 is connected with the other end of the first coupling line broadband Marchand balun 1 differential end; the other end of the third tuning transmission line 8 is connected with one end of the first blocking capacitor 9; the other end of the first blocking capacitor 9 is respectively connected with one end of the direct current bias circuit 15 and the anode of the Schottky barrier diode 10; the other end of the direct current bias circuit 15 is grounded; the cathode of the Schottky barrier diode 10 is respectively connected with one end of the second blocking capacitor 11 and one end of the second radio frequency choke inductor 19; the other end of the second radio frequency choke inductance 19 is grounded; the other end of the second blocking capacitor 11 is connected with one end of the second phase shifter 12; the other end of the second phase shifter 12 is connected with one end of a fourth tuning transmission line 13; the other end of the second tuning transmission line 13 is connected with the other end of the differential end of the second coupling line broadband Marchand balun 14.
Further, in the broadband analog predistorter, the dc bias circuit 15 includes a first rf choke inductor 16, a schottky barrier diode bias resistor 17, and a schottky barrier diode dc bias voltage 18, which are sequentially connected.
One end of the first blocking capacitor 9 is connected with one end of the first radio frequency choke inductor 16; the other end of the first radio frequency choke inductance 16 is connected with one end of the Schottky barrier diode bias resistor 17; the other end of the Schottky barrier diode bias resistor 17 is connected with one end of the Schottky barrier diode direct current bias voltage 18; the other end of the schottky barrier diode dc bias voltage 18 is grounded.
The invention has the beneficial effects that: the invention relates to a broadband analog predistorter, which specifically comprises the following components: the broadband Marchand balun comprises a first three-coupling line broadband Marchand balun, a first tuning transmission line, an attenuator, a first phase shifter, a second tuning transmission line, a third tuning transmission line, a first blocking capacitor, a Schottky barrier diode, a second blocking capacitor, a second phase shifter, a fourth tuning transmission line, a second three-coupling line broadband Marchand balun, a direct current bias circuit and a second radio frequency choke inductance. The invention adopts a three-coupling line broadband Marchand balun, an actively biased Schottky barrier diode, an attenuator and a phase shifter to form a two-way structure, the Schottky barrier diode is used as a nonlinear signal generating device, a signal is divided into two ways through the Marchand balun, one branch adopts the phase shifter and the attenuator as linear branches, the other branch adopts the Schottky barrier diode to generate nonlinear signals, the signals of the two branches are vector synthesized at the differential end of the balun, and the amplitude and the phase compensation quantity of the synthesized vector signals can be adjusted in a broadband of 4-18GHz aiming at SSPA by adjusting the bias voltage of the nonlinear branch, the attenuator and the phase shifter of the linear branch.
Drawings
Fig. 1 is a diagram of a broadband analog predistorter in accordance with the present invention.
Fig. 2 is a schematic diagram of simulation results of amplitude and phase compensation curves of the broadband analog predistorter according to an embodiment of the present invention.
Fig. 3 is a front view of a three-coupled line broadband Marchand balun in an embodiment of the present invention.
Fig. 4 is a schematic diagram of a three-coupled line broadband Marchand balun back surface structure in an embodiment of the present invention.
Fig. 5 is a schematic diagram of simulation results of broadband balun amplitude and phase curves in an embodiment of the present invention.
Detailed Description
The invention is further illustrated in the following figures and examples.
As shown in fig. 1, a wideband analog predistorter specifically includes: the broadband Marchand balun comprises a first three-coupled line broadband Marchand balun 1, a first tuning transmission line 3, an attenuator 4, a first phase shifter 5, a second tuning transmission line 6, a third tuning transmission line 8, a first blocking capacitor 9, a Schottky barrier diode 10, a second blocking capacitor 11, a second phase shifter 12, a fourth tuning transmission line 13, a second three-coupled line broadband Marchand balun 14, a direct current bias circuit 15 and a second radio frequency choke inductance 19.
The radio frequency signal is input from a first three-coupling line broadband Marchand balun 1 single port and is marked as a radio frequency signal input port 2; one end of a differential end of the first three-coupling line broadband Marchand balun 1 is connected with one end of a first tuning transmission line 3; the other end of the first tuning transmission line 3 is connected with one end of the attenuator 4; the other end of the attenuator 4 is connected with one end of the first phase shifter 5; the other end of the first phase shifter 5 is connected with one end of a second tuning transmission line 6; the other end of the second tuning transmission line 6 is connected with one end of a differential end of a second coupling line broadband Marchand balun 14; the single port of the second three-coupling line broadband Marchand balun 14 is used as a radio frequency signal output end and is marked as a radio frequency signal output port 7; one end of the third tuning transmission line 8 is connected with the other end of the first coupling line broadband Marchand balun 1 differential end; the other end of the third tuning transmission line 8 is connected with one end of the first blocking capacitor 9; the other end of the first blocking capacitor 9 is respectively connected with one end of the direct current bias circuit 15 and the anode of the Schottky barrier diode 10; the other end of the direct current bias circuit 15 is grounded; the cathode of the Schottky barrier diode 10 is respectively connected with one end of the second blocking capacitor 11 and one end of the second radio frequency choke inductor 19; the other end of the second radio frequency choke inductance 19 is grounded; the other end of the second blocking capacitor 11 is connected with one end of the second phase shifter 12; the other end of the second phase shifter 12 is connected with one end of a fourth tuning transmission line 13; the other end of the second tuning transmission line 13 is connected with the other end of the differential end of the second coupling line broadband Marchand balun 14.
In this embodiment, the wideband analog predistorter is a 4-18GHz wideband analog predistorter suitable for SSPA. The structure of the broadband analog predistorter is divided into three parts:
The first part is a first three-coupling line broadband Marchand balun 1 and a second three-coupling line broadband Marchand balun 14, the signals are divided into two paths at an input end (the first three-coupling line broadband Marchand balun 1), and the two paths of signals are synthesized and output at an output end (the second three-coupling line broadband Marchand balun 14); the second part is mainly a nonlinear branch consisting of schottky barrier diode 10; the third part is a linear branch consisting mainly of the second phase shifter 12 and the attenuator 4.
A first part: the first three-coupling-line broadband Marchand balun 1 single end is used as an input end, the differential end is used as an output end to divide signals into two paths, the second three-coupling-line broadband Marchand balun 14 differential end is used as an input, and the single end is used as the output end to synthesize and output linear branch signals and nonlinear branch signals.
A second part: one end of a first tuning transmission line 3 is connected with one end of a differential end of a first three-coupling line broadband Marchand balun 1, the other end of the first tuning transmission line 3 is connected with one end of an attenuator 4, the other end of the attenuator 4 is connected with one end of a first phase shifter 5, the other end of the first phase shifter 5 is connected with one end of a second tuning transmission line 6, and the other end of the second tuning transmission line 6 is connected with one end of a differential end of a second three-coupling line broadband Marchand balun 14.
Third section: one end of the third tuning transmission line 8 is connected with the other end of the differential end of the first third coupling line broadband Marchand balun 1, the other end of the third tuning transmission line 8 is connected with one end of the first blocking capacitor 9, the other end of the first blocking capacitor 9 is respectively connected with one end of the direct current bias circuit 15 and the anode of the Schottky barrier diode 10, the other end of the direct current bias circuit 15 is grounded, the cathode of the Schottky barrier diode 10 is respectively connected with the second blocking capacitor 11 and one end of the second radio frequency choke inductor 19, the other end of the second radio frequency choke inductor 19 is grounded, the other end of the second blocking capacitor 11 is connected with one end of the second phase shifter 12, the other end of the second phase shifter 12 is connected with one end of the fourth tuning transmission line 13, and the other end of the second tuning transmission line 13 is connected with the other end of the differential end of the second third coupling line broadband Marchand balun 14.
In this embodiment, the dc bias circuit includes a first rf choke inductor 16, a schottky barrier diode bias resistor 17, and a schottky barrier diode dc bias voltage 18, which are sequentially connected.
One end of the first blocking capacitor 9 is connected with one end of the first radio frequency choke inductor 16; the other end of the first radio frequency choke inductance 16 is connected with one end of the Schottky barrier diode bias resistor 17; the other end of the Schottky barrier diode bias resistor 17 is connected with one end of the Schottky barrier diode direct current bias voltage 18; the other end of the schottky barrier diode dc bias voltage 18 is grounded.
The impedance of the schottky barrier diode 10 is related to the magnitude of the input power of the radio frequency signal and the dc bias condition. The first radio frequency choke inductor 16, the schottky barrier diode bias resistor 17 and the schottky barrier diode direct current bias voltage 18 form a direct current bias circuit 15, the second radio frequency choke inductor 19 is used as a grounding circuit of the schottky barrier diode 10, and the distortion characteristic of nonlinear signals generated by the schottky barrier diode 10 can be adjusted by adjusting the bias voltage of the direct current bias circuit 15; the phase of the linear signal can be adjusted by adjusting the phase shift of the first phase shifter 5, and the phase of the nonlinear signal can be adjusted by adjusting the phase shift of the second phase shifter 12, and finally the linear signal and the nonlinear signal are synthesized and output through the second three-coupled line broadband Marchand balun 14, so as to generate a broadband curve for compensating the nonlinear characteristic of the SSPA.
In this embodiment, when the wideband analog predistorter works, an input signal of the radio frequency signal input port 2 is input into the first third coupled line wideband Marchand balun 1 through a single port, and two paths of differential signals are output at a differential port: the output signal at one end of the differential port obtains a linear signal with amplitude and phase change through the attenuator 4 and the first phase shifter 5; the other end of the differential port is loaded on the Schottky barrier diode 10 through the first blocking capacitor 9, and the nonlinear condition of the corresponding branch is changed by utilizing the nonlinear change of the input impedance of the Schottky barrier diode 10 along with the input power. The signal of the nonlinear branch and the signal of the linear branch are synthesized at the differential end of the second three-coupling-line broadband Marchand balun 14, and the final nonlinear signal is output by the radio frequency signal output port 7.
FIG. 2 is a schematic diagram of simulation results of the amplitude and phase compensation curve of the broadband analog predistorter in the present embodiment, and the abscissa Pin represents the input power in dBm; the ordinate Gain represents Gain in dB; the ordinate Phase represents Phase in degrees.
Wherein, fig. 2 (a) is an amplitude characteristic phase curve at 4GHz, 11GHz and 18GHz when the bias voltage is 0.3V, the attenuation amount of the attenuator is 20dB, the first phase shifter is-100 °, and the second phase shifter is 0 °, as can be seen from the figure, the amplitude expansion of at least 4.5dB is realized from 4GHz to 18 GHz; fig. 2 (b) shows phase characteristic phase curves at 4GHz, 11GHz and 18GHz under the same conditions, and it can be seen from the figure that the amplitude expansion of at least 30 ° is achieved from 4GHz to 18 GHz.
In this embodiment, the first three-coupled-line broadband Marchand balun 1 and the second three-coupled-line broadband Marchand balun 14 have the same structure, as shown in fig. 3 and fig. 4.
Fig. 3 is a front structure diagram of a three-coupled-line broadband Marchand balun, fig. 4 is a rear structure diagram of the three-coupled-line broadband Marchand balun, and fig. 3 includes: the three-coupling-line microstrip broadband balun comprises a metallized through hole 20, a three-coupling-line microstrip broadband balun single port 21, a three-coupling-line microstrip broadband balun substrate 22, a first coupling microstrip line 23, a second coupling microstrip line 24, a three-coupling-line microstrip broadband balun first differential port 25, a three-coupling-line microstrip broadband balun second differential port 26 and a gold wire 27; in fig. 3, L1 is the length of the microstrip substrate, L2 is the 1/4 wavelength coupled microstrip, W1 is the width of the ground portion Pad, and W2 is the length of the differential port.
The radio frequency signal is input from the three-coupling-line microstrip broadband balun single port 21, is coupled with the first coupling microstrip line 23 and the second coupling microstrip line 24, and is output from the three-coupling-line microstrip broadband balun first differential port 25 and the three-coupling-line microstrip broadband balun second differential port 26, so that the effect of power division is realized.
FIG. 5 is a schematic diagram of simulation results of broadband balun amplitude and phase curves, with the abscissa freq representing frequency in Ghz; the ordinate dB (S (2, 1)) represents gain in dB; the ordinate Phase represents Phase in degrees.
Wherein, fig. 5 (a) shows the attenuation of broadband balun output relative to input, it can be seen that the attenuation from 4GHz to 18GHz is about 3dB, and a better power division effect is realized in a broadband; fig. 5 (b) shows that the phase change with respect to frequency is seen as a linear phase, and the phases of the differential ports are 180 ° out of phase.
In summary, it can be seen that, in the broadband analog predistorter structure of this embodiment, by changing the circuit bias state and the phase shifter and the phase shift amount, the distortion characteristic of the SSPA can be compensated, and compared with the existing two-way circuit structure, the two-way structure of the broadband balun is adopted, so that the frequency band of the analog predistorter is wider. The invention adopts a nonlinear branch composed of three coupled line broadband Marchand balun and an active bias Schottky barrier diode and a linear branch composed of a phase shifter and an attenuator to form a two-way structure, the Schottky barrier diode is used as a nonlinear signal generating device, so that the circuit structure becomes simpler, a signal is divided into two ways through the Marchand balun, one branch adopts the Schottky barrier diode to generate a nonlinear distorted signal, the other branch utilizes the phase shifter and the attenuator to generate a linear signal, the signals of the two branches are vector synthesized at the Marchand balun differential end, and the amplitude phase adjustment can be realized in a broadband through adjusting the nonlinear bias voltage and the phase shift of the phase shifter.
Those of ordinary skill in the art will recognize that the embodiments described herein are for the purpose of aiding the reader in understanding the principles of the present invention and should be understood that the scope of the invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various other specific modifications and combinations from the teachings of the present disclosure without departing from the spirit thereof, and such modifications and combinations remain within the scope of the present disclosure.
Claims (3)
1. A broadband analog predistorter specifically comprises: the broadband Marchand balun comprises a first three-coupling line broadband Marchand balun (1), a first tuning transmission line (3), an attenuator (4), a first phase shifter (5), a second tuning transmission line (6), a third tuning transmission line (8), a first blocking capacitor (9), a Schottky barrier diode (10), a second blocking capacitor (11), a second phase shifter (12), a fourth tuning transmission line (13), a second three-coupling line broadband Marchand balun (14), a direct current bias circuit (15) and a second radio frequency choke inductance (19);
The radio frequency signal is input from a single port of a first three-coupling-line broadband Marchand balun (1), and is marked as a radio frequency signal input port (2); one end of a differential end of the first three-coupling line broadband Marchand balun (1) is connected with one end of a first tuning transmission line (3); the other end of the first tuning transmission line (3) is connected with one end of the attenuator (4); the other end of the attenuator (4) is connected with one end of the first phase shifter (5); the other end of the first phase shifter (5) is connected with one end of a second tuning transmission line (6); the other end of the second tuning transmission line (6) is connected with one end of a differential end of a second coupling line broadband Marchand balun (14); the single port of the second three-coupling line broadband Marchand balun (14) is used as a radio frequency signal output end and is marked as a radio frequency signal output port (7); one end of a third tuning transmission line (8) is connected with the other end of the differential end of the first coupling line broadband Marchand balun (1); the other end of the third tuning transmission line (8) is connected with one end of the first blocking capacitor (9); the other end of the first blocking capacitor (9) is respectively connected with one end of the direct current bias circuit (15) and the anode of the Schottky barrier diode (10); the other end of the direct current bias circuit (15) is grounded; the cathode of the Schottky barrier diode (10) is respectively connected with one end of the second blocking capacitor (11) and one end of the second radio frequency choke inductor (19); the other end of the second radio frequency choke inductance (19) is grounded; the other end of the second blocking capacitor (11) is connected with one end of the second phase shifter (12); the other end of the second phase shifter (12) is connected with one end of a fourth tuning transmission line (13); the other end of the second tuning transmission line (13) is connected with the other end of the differential end of the second coupling line broadband Marchand balun (14).
2. A broadband analog predistorter according to claim 1, characterized in that in the broadband analog predistorter, the dc bias circuit (15) comprises a first radio frequency choke inductance (16), a schottky barrier diode bias resistance (17), a schottky barrier diode dc bias voltage (18) connected in sequence;
One end of the first blocking capacitor (9) is connected with one end of the first radio frequency choke inductor (16); the other end of the first radio frequency choke inductor (16) is connected with one end of a Schottky barrier diode bias resistor (17); the other end of the Schottky barrier diode bias resistor (17) is connected with one end of the Schottky barrier diode direct current bias voltage (18); the other end of the Schottky barrier diode is grounded by a direct current bias voltage (18).
3. A broadband analog predistorter according to claim 1, characterized in that, when the broadband analog predistorter is in operation, the input signal of the radio frequency signal input port (2) is input to the first three-coupled-line broadband Marchand balun (1) through a single port, and two differential signals are output at differential ports: an output signal at one end of the differential port obtains a linear signal with amplitude and phase change through an attenuator (4) and a first phase shifter (5); the other end of the differential port is loaded on the Schottky barrier diode (10) through the first blocking capacitor (9), and the nonlinear condition of the corresponding branch is changed by utilizing the nonlinear change of the input impedance of the Schottky barrier diode (10) along with the input power; the signal of the nonlinear branch and the signal of the linear branch are synthesized at the differential end of the second three-coupling line broadband Marchand balun (14), and the final nonlinear signal is output by the radio frequency signal output port (7).
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